On some classes of inverse problems with overdetermination data on spatial manifolds

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• 作者：S. G. Pyatkov
• 关键词：parabolic system ; inverse problem ; initial ; boundary value problem ; well ; posedness ; unconditional solvability
• 刊名：Siberian Mathematical Journal
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：57
• 期：5
• 页码：870-880
• 全文大小：235 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260
• 卷排序：57

文摘

We consider the question of well-posedness of the inverse problems of determining the righthand side (a source function) of a special form of a parabolic system of equations. The overdetermination data are the values of a solution and its normal derivatives on a system of surfaces in a spatial domain. In particular, the cross-sections of the domain can be used as these surfaces. Sharp conditions are presented for the data of the problem to ensure well-posedness.